Limited-Feedback Low-Encoding Complexity Precoder Design for Downlink of FDD Multi-User Massive MIMO Systems

Abstract

We investigate a limited feedback precoder based on symbol pairwise error probability (PEP) for a block-faded $K \times n_{t}$ downlink multiple-input multiple-output (MIMO) channel. In the considered system, $K=\lfloor n_{t}^{\alpha }\rfloor $ single-antenna users feedback quantized channel state information to the $n_{t}$ -antenna transmitter using $B$ bits per-transmit-antenna per user. We analytically show that for $\alpha , $B \geq 1$ and $n_{t}\rightarrow \infty $ , both symbol PEP and achievable rate of each of the $K$ downlink users almost surely converge to the symbol PEP and achievable rate of $K$ parallel additive white Gaussian noise (AWGN) channels, respectively. We show that the encoding complexity of the precoder is $O(n_{t}K)$ . We also show that if channel coefficients estimated by the user are corrupted by AWGN noise, the symbol PEP and achievable rate of each user almost surely converge to the symbol PEP and achievable rate in a scaled AWGN channel with $B>1$ and $n_{t}\rightarrow \infty $ . For correlated channels, we derive a condition, which enables the proposed precoder almost surely to cancel multi-user interference for large $n_{t}$ values. Finally, we numerically compare the bit error rate, encoding complexity, and per-user achievable rate of the proposed scheme with the existing designs.